Momentum space and Minkowski diagrams are powerful tools for interpreting and analysing relativistic collisions in one or two spatial dimensions. All relevant quantities that characterize a collision, including the mass, velocity, momentum and energy of the interacting particles, both before and after collision, can be directly seen from a single Minkowski diagram. Such diagrams can also be useful for analysing the differences between Newtonian and relativistic mechanics. As an interesting example, a simple derivation of the Compton wavelength shift formula, based on the geometrical properties of such momentum space diagrams, is also presented. (Contains 5 figures.)